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The Mexican won from pole position for Red Bull on Sunday.
The Mexican triumphed in a rain-delayed race that saw Ferrari's Charles Leclerc finish second.
The Dutchman finished 17.8 seconds ahead of his Mexican team mate Sergio Perez.
Mexican Sergio Perez, winner of the previous race in Monaco, was second on the streets of Baku.
The Mexican's teammate Max Verstappen finished third to stretch his Formula One championship lead over Leclerc.
A tyre blowout denied Max Verstappen victory and Lewis Hamilton failed to score.
The Mexican said he was adjusting to his surroundings after seven years with the Force India/Racing Point team that is now Aston Martin.
The Formula One team finally confirmed on Thursday that Perez would continue racing for them in 2019.
Germany's Nico Hulkenberg will replace Perez at Sunday's British Grand Prix.
The 33-year-old German replaces Mexican Sergio Perez at the team formerly known as Racing Point.
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